In the past, avionics engineers have endeavored to change the operation of a mobile transceiver depending upon the location of the transceiver with respect to the boundaries of geographic areas which have predetermined exposure to satellite signals for satellite communication. These predetermined geographic areas are often referred to as spot beams. If an aircraft is within the spot beam, the satellite communication transceiver will be operated differently than if it is outside of a spot beam. However, since aircraft travel at relatively high velocity, they may enter and exit several spot beams during a single flight. In the past, determining whether the aircraft is in a spot beam has often taken considerable time and consumed valuable computing resources on the aircraft.
One well-known approach has been to draw a line from the given point to any point that is known to be outside of the spot beam boundary (polygon), e.g. to infinity, and then counting the number of times the line intersects the polygon boundary. If the number of intersections is odd, then the given point is inside the polygon. If the number of intersections is even, then the point is outside the polygon. The same method can be applied to spherical coordinates; i.e. let the North Pole be the point outside of the polygon; this can be assumed for the case of a geo-stationary satellite spot beam.
However, some of these prior art methods do not always accurately determine the presence of the aircraft within a spot beam, especially with respect to intersections occurring at vertices of the line segments of the polygon.
Consequently, there exists a need for improvement in methods and apparatuses for determining whether a mobile transceiver is within a spot beam.